In the still of Baghdad's hot midnight, among thick palm groves that line the Diala river to the city's south, the sound of helicopters strafing the tree line a few hundred metres distant seems sickeningly close.

The Apache gunships are invisible except for the bright commas of gunfire that appear for the briefest of moments. The noise catches up, an ugly bass drilling sound that jars even the US soldiers in their vehicles and uniforms marked to be visible from the air.

It is not quite random firing into the farmland and groves. It is a calling card to the mortar teams who use these secluded spots to fire into the distant Green Zone. An hour or so earlier, it was artillery firing out of one of the forward operating bases, the explosions echoing among the tall, spare trees.

The soldiers call it 'area denial'. When a shell overshoots its target by 600 metres, it scatters razor-sharp fragments across the roofs of the nearby houses.

This weekend the firing has an extra urgency. Following tips from Iraqi civilians, the hunt is on for a new and deadlier kind of rocket, modelled on one of those used by Hizbollah, the al-Sharooq.

In the pictures the soldiers have been given it looks like an artillery shell with jet boosters, fired out of its own launcher. It can fly six miles with an accuracy far greater than any of the rockets or mortars deployed so far. It can penetrate armour and the hardened shelters of the Green Zone - a new and dangerous escalation in the war in Iraq. Tonight, sources say, it will be fired for the first time.

'It is like searching for a needle in a haystack,' says Lieutenant Johnathan Lee of the 2/17 Field Artillery, leading a patrol of Humvee vehicles along the small, rough dirt roads that intersect the palm groves in the hope of catching a rocket team in the act of firing. But that is not all. His presence on the ground, talking to the farmers and drivers he encounters, is also designed to discourage the mortar teams. It is the human face of 'area denial'.

Lee, 24, is not certain whether the tips are bad intelligence meant as sabotage or simply a rumour that has become inflated in the telling. If mortars are fired, he explains politely to any Iraqis he encounters, the gun crews will detect the source and fire back. Then there is the risk that civilians will be hurt.

The alternative, he says, is to tell his forces when the mortar teams are in the area. Then life will improve. But many Iraqis still regard the Americans as the aggressors and shield the mortar teams. Others are simply afraid of retaliation from militant groups, both Shia and Sunni.

It is a Catch-22. The soldiers try to stop the rockets before they are fired, but in reality the best way to catch the rocket teams is after their cargoes of metal and explosives are already arcing through the air.

Lee stops at a compound in the woods and two men appear out of the darkened house, Sunni farmers who tend the groves. Lee asks if they have seen men bringing mortars into the woods. After some thought, they agree that they have. The people on the 'other side of the river', they say, their Shia neighbours in an area split 80-20 in favour of Shias.

The two men, who refuse to give their names, saw a mortar team in their woods 10 days ago, four bearded men in dishdashas, driving a Chinese pick-up truck and carrying guns. 'It is not strange to see something like this round here,' said the first man. 'A car with a Baghdad plate. It came from the direction of al-Butal [a bottling factory]. There are a lot of militias there. There are bad people there.'

The 'bad people' by their account are Shia gangs who have kidnapped and murdered Sunni men. The same people are responsible for the rockets.

It is dangerous for the American soldiers to linger too long after dark on their anti-mortar and rocket patrols. The night before it had been a different neighbourhood, Zafraniya, where we had been searching for the mortar teams, not in the woods this time but in an area of rough, dusty football pitches enclosed by poor housing on all sides.

A few men appear through a set of double doors in a nearby alley. At first it appears that they are hanging out like so many do in Iraq's high summer - so often lacking in electricity and therefore air-conditioning - when only the night is bearable for sitting out and talking.

Then, just as they are spotted, one produces a rocket-propelled grenade and fires it so close to our vehicle that it forces the gunner, Sergeant Fred Pedro, to duck. It is the militants' way of delivering their own message: don't come hunting in our neighbourhoods.

And the hunt for the mortar tubes - which can fire and be gone in less than two minutes - is full of lethal paradoxes. 'What sucks in trying to counter mortar teams,' says Captain Chris Halstead, 'is you need them to fire a few times. You need to know pattern. And that means there is the risk someone will get killed.

'The teams know too that we have to operate under restraints in built-up areas over the way we can return fire. And looking at it from the outside, they are methodical, quick, and they use the mortar fire to keep people off-balance.' A little later several mortars land at the nearby US base at Rustamiya from one of Zafraniya's neighbourhoods - or muhallas. 'We patrol the scrubland. Then they fire from inside muhallas,' says an exasperated Captain Dave Smith, who is responsible for liaising with the local neighbourhood council. He grabs a phone and begins the process of calling each of the council members in the areas from where the mortars came. One feigns ignorance, saying he was in his house. Another claims he thought the detonations 'were a wedding celebration'.

'We have two enduring operations here,' Smith says. 'They are called Happy Town and Sad Town. Any time we cause any damage with counter fire to mortar launches we go in and assess the damage, test the atmospherics and ask people why they allowed mortars to fire from by their houses. We hand out claim cards and try to placate the locals. That is Happy Town. In Operation Sad Town, we lock down the neighbourhood. We search houses and wake people up. We put pressure on people. We have the psy-op [psychological operations] truck go round broadcasting. But there are always people who will just say: "Oh? We didn't hear the explosion when the mortar was launched."'